We determine the structure of Hopf algebras that admit an extension of a group algebra by the cyclic group of order 2. We study the corepresentation theory of such Hopf algebras, which provide a generalization, at the Hopf algebra level, of the so called Tambara-Yamagami fusion categories. As a byproduct, we show that every semisimple Hopf algebra of dimension < 36 is necessarily group-theoreti...

We study cohomology theories of strongly homotopy algebras, namely A∞, C∞ and L∞-algebras and establish the Hodge decomposition of Hochschild and cyclic cohomology of C∞-algebras thus generalising previous work by Loday and Gerstenhaber-Schack. These results are then used to show that a C∞-algebra with an invariant inner product on its cohomology can be uniquely extended to a symplectic C∞-alge...

In the present paper we prove a statement closely related to the cyclic formality conjecture [Sh]. In particular, we prove that for a volume form Ω and a Poisson bivector field π on Rd such that divΩ π = 0, the Kontsevich star-product [K] with the harmonic angle function is cyclic, i.e. ∫ Rd (f ∗ g) · h · Ω = ∫ Rd (g ∗ h) · f · Ω for any three functions f, g, h on Rd (for which the integrals ma...

We prove that every action of a finite group all of whose Sylow subgroups are cyclic on the K-theory of a Kirchberg algebra can be lifted to an action on the Kirchberg algebra. The proof uses a construction of Kirchberg algebras generalizing the one of Cuntz-Krieger algebras, and a result on modules over finite groups. As a corollary, every automorphism of the K-theory of a Kirchberg algebra ca...

A new class of coefficients for the Hopf-cyclic homology of module algebras and coalgebras is introduced. These coefficients, termed stable anti-Yetter-Drinfeld contramodules, are both modules and contramodules of a Hopf algebra that satisfy certain compatibility conditions. 1. Introduction. It has been demonstrated in [8], [9] that the Hopf-cyclic homology developed by Connes and Moscovici [5]...

Lie transformation groups containing a one-dimensional subgroup acting cyclically on a manifold are considered. The structure of the group is found to be considerably restricted by the existence of a one-dimensional subgroup whose orbits are circles. The results proved do not depend on the dimension of the manifold nor on the existence of a metric, but merely on the fact that the Lie group acts...

We prove that for any two commuting von Neumann algebras of infinite type, the open set of Bell correlated states for the two algebras is norm dense. We then apply this result to algebraic quantum field theory — where all local algebras are of infinite type — in order to show that for any two spacelike separated regions, there is an open dense set of field states that dictate Bell correlations ...

For given Banach algebras A and B, we define a free resolution of algebraB over a homomorphism f : A → B and study some properties of the relative cyclic homology.

We give a construction of a nuclear C∗-algebra associated with an amalgamated free product of groups, generalizing Spielberg’s construction of a certain Cuntz-Krieger algebra associated with a finitely generated free product of cyclic groups. Our nuclear C∗-algebras can be identified with certain Cuntz-Krieger-Pimsner algebras. We will also show that our algebras can be obtained by the crossed ...

We introduce the notion of ends for algebras. The definition is analogous to the one in geometric group theory. We establish some relations to growth conditions and cyclic cohomology.